We study Hadamard variations with respect to general domain perturbations, particularly for the Neumann boundary condition. They are derived from new Liouville's formulae concerning the transformation of volume and area integrals. Then, relations to several geometric quantities are discussed; differential forms and the second fundamental form on the boundary.
{"title":"Liouville's formulae and Hadamard variation with respect to general domain perturbations","authors":"Takashi Suzuki, T. Tsuchiya","doi":"10.2969/jmsj/88958895","DOIUrl":"https://doi.org/10.2969/jmsj/88958895","url":null,"abstract":"We study Hadamard variations with respect to general domain perturbations, particularly for the Neumann boundary condition. They are derived from new Liouville's formulae concerning the transformation of volume and area integrals. Then, relations to several geometric quantities are discussed; differential forms and the second fundamental form on the boundary.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42515682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Robustness of exponential attractors for infinite dimensional dynamical systems with small delay and application to 2D nonlocal diffusion delay lattice systems","authors":"Lin Yang, Yejuan Wang, P. Kloeden","doi":"10.2969/jmsj/88438843","DOIUrl":"https://doi.org/10.2969/jmsj/88438843","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42121880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Generalizing work of I. Baykur, K. Hayano, and N. Monden (arXiv:1903.02906), we construct infinite families of symplectic 4-dimensional manifolds, obtained as total spaces of Lefschetz pencils constructed by explicit monodromy factorizations. Then, generalizing work of the author (arXiv:2108.04868), we show that each of these manifolds is diffeomorphic to a complex surface that is a fiber sum formed from two standard examples of hyperelliptic Lefschetz fibrations. Consequently, we see that these hyperelliptic Lefschetz fibrations, as well as all fiber sums of them, admit an infinite family of explicitly described Lefschetz pencils, which we observe are different from families formed by the degree doubling procedure.
{"title":"Branched covers and pencils on hyperelliptic Lefschetz fibrations","authors":"Terry Fuller","doi":"10.2969/jmsj/90089008","DOIUrl":"https://doi.org/10.2969/jmsj/90089008","url":null,"abstract":"Generalizing work of I. Baykur, K. Hayano, and N. Monden (arXiv:1903.02906), we construct infinite families of symplectic 4-dimensional manifolds, obtained as total spaces of Lefschetz pencils constructed by explicit monodromy factorizations. Then, generalizing work of the author (arXiv:2108.04868), we show that each of these manifolds is diffeomorphic to a complex surface that is a fiber sum formed from two standard examples of hyperelliptic Lefschetz fibrations. Consequently, we see that these hyperelliptic Lefschetz fibrations, as well as all fiber sums of them, admit an infinite family of explicitly described Lefschetz pencils, which we observe are different from families formed by the degree doubling procedure.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48163694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let p be an odd prime number and 2e+1 be the highest power of 2 dividing p − 1. For 0 ≤ n ≤ e, let kn be the real cyclic field of conductor p and degree 2n. For a certain imaginary quadratic field L0, we put Ln = L0kn. For 0 ≤ n ≤ e − 1, let Fn be the imaginary quadratic subextension of the imaginary (2, 2)-extension Ln+1/kn with Fn ̸= Ln. We study the Galois module structure of the 2-part of the ideal class group of the imaginary cyclic field Fn. This generalizes a classical result of Rédei and Reichardt for the case n = 0.
{"title":"On the class groups of certain imaginary cyclic fields of 2-power degree","authors":"H. Ichimura, Hiroki Sumida-Takahashi","doi":"10.2969/jmsj/86438643","DOIUrl":"https://doi.org/10.2969/jmsj/86438643","url":null,"abstract":"Let p be an odd prime number and 2e+1 be the highest power of 2 dividing p − 1. For 0 ≤ n ≤ e, let kn be the real cyclic field of conductor p and degree 2n. For a certain imaginary quadratic field L0, we put Ln = L0kn. For 0 ≤ n ≤ e − 1, let Fn be the imaginary quadratic subextension of the imaginary (2, 2)-extension Ln+1/kn with Fn ̸= Ln. We study the Galois module structure of the 2-part of the ideal class group of the imaginary cyclic field Fn. This generalizes a classical result of Rédei and Reichardt for the case n = 0.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69573974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we prove that a free abelian group cannot occur as the group of self-homotopy equivalences of a rational CW-complex of finite type. Thus, we generalize a result due to Sullivan-Wilkerson showing that if X is a rational CW-complex of finite type such that dimH∗(X,Z) < ∞ or dimπ∗(X) < ∞, then the group of self-homotopy equivalences of X is isomorphic to a linear algebraic group defined over Q.
{"title":"The group of self-homotopy equivalences of a rational space cannot be a free abelian group","authors":"M. Benkhalifa","doi":"10.2969/jmsj/87158715","DOIUrl":"https://doi.org/10.2969/jmsj/87158715","url":null,"abstract":"In this paper, we prove that a free abelian group cannot occur as the group of self-homotopy equivalences of a rational CW-complex of finite type. Thus, we generalize a result due to Sullivan-Wilkerson showing that if X is a rational CW-complex of finite type such that dimH∗(X,Z) < ∞ or dimπ∗(X) < ∞, then the group of self-homotopy equivalences of X is isomorphic to a linear algebraic group defined over Q.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45081143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the sheaf-theoretic $operatorname{SL}(2,mathbb{C})$ Casson–Lin invariant","authors":"Lauren Cote, Ikshu Neithalath","doi":"10.2969/jmsj/84808480","DOIUrl":"https://doi.org/10.2969/jmsj/84808480","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45806430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Factors of $E$-operators with an $eta$-apparent singularity at zero","authors":"T. Rivoal","doi":"10.2969/jmsj/85708570","DOIUrl":"https://doi.org/10.2969/jmsj/85708570","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45425087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Moduli of Gorenstein $mathbb{Q}$-homology projective planes","authors":"M. Schütt","doi":"10.2969/jmsj/87028702","DOIUrl":"https://doi.org/10.2969/jmsj/87028702","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43551244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
One of the important research subjects in the study of multiple zeta functions is to clarify the linear relations and functional equations among them. The Schur multiple zeta functions are a generalization of the multiple zeta functions of Euler-Zagier type. Among many relations, the duality formula and its generalization are important families for both Euler-Zagier type and Schur type multiple zeta values. In this paper, following the method of previous works for multiple zeta values of Euler-Zagier type, we give an interpolation of the sums in the generalized duality formula, called Ohno relation, for Schur multiple zeta values. Moreover, we prove that the Ohno relation for Schur multiple zeta values is valid for complex numbers.
{"title":"An interpolation of the generalized duality formula for the Schur multiple zeta values to complex functions","authors":"Maki Nakasuji, Yasuo Ohno, Wataru Takeda","doi":"10.2969/jmsj/89978997","DOIUrl":"https://doi.org/10.2969/jmsj/89978997","url":null,"abstract":"One of the important research subjects in the study of multiple zeta functions is to clarify the linear relations and functional equations among them. The Schur multiple zeta functions are a generalization of the multiple zeta functions of Euler-Zagier type. Among many relations, the duality formula and its generalization are important families for both Euler-Zagier type and Schur type multiple zeta values. In this paper, following the method of previous works for multiple zeta values of Euler-Zagier type, we give an interpolation of the sums in the generalized duality formula, called Ohno relation, for Schur multiple zeta values. Moreover, we prove that the Ohno relation for Schur multiple zeta values is valid for complex numbers.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69574321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, when a given symmetric Markov process X satisfies the stability of global heat kernel two-sided (upper) estimates by Markov perturbations (See Definition 1.2), we give a necessary and sufficient condition on the stability of global two-sided (upper) estimates for fundamental solution of Feynman-Kac semigroup of X. As a corollary, under the same assumptions, a weak type global two-sided (upper) estimates holds for the fundamental solution of Feynman-Kac semigroup with (extended) Kato class conditions for measures. This generalizes all known results on the stability of global integral kernel estimates by symmetric Feynman-Kac perturbations with Kato class conditions in the framework of symmetric Markov processes.
{"title":"Stability of estimates for fundamental solutions under Feynman–Kac perturbations for symmetric Markov processes","authors":"Daehong Kim, P. Kim, K. Kuwae","doi":"10.2969/jmsj/88038803","DOIUrl":"https://doi.org/10.2969/jmsj/88038803","url":null,"abstract":"In this paper, when a given symmetric Markov process X satisfies the stability of global heat kernel two-sided (upper) estimates by Markov perturbations (See Definition 1.2), we give a necessary and sufficient condition on the stability of global two-sided (upper) estimates for fundamental solution of Feynman-Kac semigroup of X. As a corollary, under the same assumptions, a weak type global two-sided (upper) estimates holds for the fundamental solution of Feynman-Kac semigroup with (extended) Kato class conditions for measures. This generalizes all known results on the stability of global integral kernel estimates by symmetric Feynman-Kac perturbations with Kato class conditions in the framework of symmetric Markov processes.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49646588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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